Granger-Causal Analysis of VARMA-GARCH Models

Abstract

Recent economic developments have shown the importance of spillover and contagion effects in financial markets. Such effects are not limited to relations between the levels of financial variables but also impact on their volatility. I investigate Granger causality in conditional mean and conditional variances of time series. For this purpose a VARMA-GARCH model is used. I derive parametric restrictions for the hypothesis of noncausality in conditional variances between two groups of variables, when there are other variables in the system as well. These novel conditions are convenient for the analysis of potentially large systems of economic variables. Such systems should be considered in order to avoid the problem of omitted variable bias. Further, I propose a Bayesian Lindley-type testing procedure in order to evaluate hypotheses of noncausality. It avoids the singularity problem that may appear in the Wald test. Also, it relaxes the assumption of the existence of higher-order moments of the residuals required for the derivation of asymptotic results of the classical tests. In the empirical example, I find that the dollar-to-Euro exchange rate does not second-order cause the pound-to-Euro exchange rate, in the system of variables containing also the Swiss frank-to-Euro exchange rate, which confirms the meteor shower hypothesis of Engle, Ito & Lin (1990).